What is the present value of $3,800 at 8.9 percent compounded monthly for five years.
Thurs far, I have P= ?/(1+i)n
(1 + 0.89/12)12*5
(1.0074167)60
P = Po(1+r)^n
P = $3,800
r = (8.9%/12)/100% = 0.00742 = Monthly %
rate expressed as a decimal.
n = 12comp./yr. * 5yrs.=60 Compounding
periods.
P = Po(1+0.00742)^60 = 3800
Po*(1.00742)^60 = 3800
Po = 3800/(1.00742)^60 = $2438.65 =
Present value.
To calculate the present value of a future amount, you can use the formula:
Present Value (P) = Future Value (F) / (1 + interest rate (i)) ^ time period (n)
In this case, the future value (F) is $3,800, the interest rate (i) is 8.9% (which needs to be converted to a decimal, so i = 0.089), and the time period (n) is 5 years.
Now, let's use the formula to calculate the present value:
P = $3,800 / (1 + 0.089) ^ 5
First, calculate inside the brackets:
(1 + 0.089) ^ 5 = (1.089) ^ 5 = 1.48814989
Now, divide the future value by this result:
P = $3,800 / 1.48814989
Performing the division:
P ≈ $2,551.732
Therefore, the present value of $3,800 at 8.9% compounded monthly for five years is approximately $2,551.732.